How to build a Evol

Remember how small but fearless Pinocchio won the most terrible Karabas-Barabas? The villain caught his long beard in a knot when running over a wooden man around the tree. The trajectory described by the Director of the puppet theatre – the involute of a circle or flattened circle. The processed involute teeth of gear wheels and gears. So to be able to build such a curve should every engineer.

You will need

• A sheet of paper, pencil, compass, ruler, French curve, square

Instruction

1. Place a piece of paper so that the long side was laid along the edge of the table. Mentally divide it horizontally and vertically into 4 parts. About the middle of the upper right part put a point O. the Compass, draw a circle of a given radius, with its center at the point O.
2. In the upper part of the circle, somewhere in the 12 hours put a dot and label it figure 12. In point 12, place a compass, the distance between the legs which is equal to the radius R of the circle. Make the compass notches on the circumference. The notch on the right indicate 2, and the left - 10. In the same way, make the incision from points 2 and 10. A notch down from point 2 to point 4 and down from point 10 to point 8. From point 4, similarly constructed notch - a point 6.
3. Connect the dots 12 and 6 with a straight line. And build on it using a square the perpendicular passing through the point O. the Point of intersection of the circle and perpendicular to the left indicate the digit 9, and the right figure 3.
4. The notch on the circle made by a compass from point 3 at the top mark with a number 1, and the bottom – 5. And the incisions made from the point 9, – figures 11 and 7.
5. Each numbered point on the line segment connect center of the circle. The end result is a circle that is broken, like a clock into 12 equal sectors.
6. From the point 12 to the left, construct a tangent to a circle, i.e. a line perpendicular to the radius. Similarly, take tangents through all other points.
7. Calculate circumference by the formula: L=2nr, where π≈3,14. And find the 1/12 part of the circumference of a circle: Lₒ=L/12.
8. From the point 12 at a tangent put a period equal to 11•Lₒ and set point B12.
9. From point 11 at a tangent put a segment of length 10•Lₒ. Put a point Q11.
10. Point-10 – segment 9•Lₒ. Put a dot at 10. And so on. Point 1 and point B1 coincide.
11. Curve connect the points B1, B2, ... B12. The curve is the involute of the circle.